The walls have been covered in silk, the ceiling cove painted albacore, and old skylights replaced with triple-glazed glass. But when the Museum of Fine Arts reopens its large Dutch and Flemish gallery on Wednesday, the buzz won’t just be about the paintings hanging on the walls — alluring as they are — but on a bigger trove of masterworks that could possibly one day join them.

That’s because 17 of the paintings in this and a recently reopened gallery nearby belong to Eijk and Rose-Marie van Otterloo, the longtime Marblehead residents who have amassed arguably the world’s greatest private collection of 17th-century Dutch and Flemish art. And the van Otterloos say they are close to deciding which museum will be the permanent home of a collection worth hundreds of millions of dollars, featuring works by Rembrandt and Frans Hals, among others.

That tantalizing prospect has set off a very quiet and studiously polite competition among some of the nation’s leading museums, a courtship minuet in which no one can afford to seem as covetous as they are.

“It would transform any museum it was given to,” said MFA director Malcolm Rogers, one of the museum leaders vying for the works. “I cannot preempt their decision or read their minds. But I think the MFA would make a marvelous setting for their collection.”

That the van Otterloos feel they must decide on their collection’s future is not out of the ordinary in the world of major collectors. What is notable is the openness with which they are discussing that process.

The couple, who lived until recently in Marblehead but now spend most of the year in Naples, Fla., are still active collectors. But Rose-Marie, 67, said in an exclusive interview last week that, largely on the advice of the financial advisor assisting them with estate planning, they will make a decision in the next two years.

She names five contenders: The MFA, the Peabody Essex Museum, the National Gallery of Art in Washington, the Harvard Art Museums, and the Huntington Library, Art Collections, and Botanical Gardens in San Marino, Calif. There could be others.

“I am not going to call the Art Institute of Chicago, but if the Art Institute of Chicago comes to us and said, ‘We want to talk,’ we will listen,” she said.

One decision has already been made, however. Even though one of their masterworks, a Salomon van Ruysdael river view, hangs in the famed “Gallery of Honour” of the recently reopened Rijksmuseum in Amsterdam, Rose-Marie said the couple have ruled out giving the works to a museum in the Netherlands.

“We really think Holland has all it needs,” she said.

Eijk van Otterloo, born in the Netherlands, helped found an investment firm that manages more than $100 billion. He met Rose-Marie, a native of Belgium, on a blind date in 1973, and after they married, the couple moved to the North Shore in 1976. They began collecting Dutch and Flemish art in the early 1990s.

There has been speculation for years about the couple’s collection, which includes about 70 paintings, more than 20 pieces of furniture, and 10,000 Dutch art history books. Two years ago, the Peabody Essex Museum mounted a massive show featuring the couple’s paintings and furniture.

Eijk, now 76, said in a Globe interview at the time that if he had been ready to give the collection away then, it would probably go to the MFA. Last week, in an interview at her former home in Marblehead — the couple have placed the art-filled waterfront spread in a trust for their children — Rose-Marie backed away from that.

“I think he probably said it because Boston is, after all, the place that has Dutch and Flemish art, but for the same reason he could have said Harvard because Harvard also has a beautiful collection of Dutch art,” she said. “If you think of the Peabody Essex, they have no Dutch art, so it might be nice for Peabody Essex to have a collection. So who? At this point, we really don’t know.”

For local museum leaders, the van Otterloos are already known well for their connoisseurship and their exceptional generosity. The MFA has, over the years, received gifts from them of 278 works of art, primarily European prints and drawings, including five works by Rembrandt. They are titled by the museum as “eminent benefactors,” a level meant to note $5 million to $10 million in gifts over the years.

Eijk, a former MFA trustee, is a member of the museum’s art of Europe visiting committee. Rose-Marie, currently an MFA trustee, chairs the MFA’s collections committee and is a member of the conservation and collections management visiting committee and the art of Europe visiting committee.

The couple also paid an undisclosed sum for the MFA’s current Dutch and Flemish gallery renovations. They agreed to that request “in five minutes,” said Rose-Marie, after Rogers called them in Naples.

The large gallery was closed for 11 months for renovation and will reopen Wednesday, while the smaller nearby gallery was closed briefly so its works could be reinstalled. The galleries include loaned works from the van Otterloo collection with paintings from the MFA collection by Peter Paul Rubens, Gerrit Dou, and Jan Both.

The centerpiece of the van Otterloo collection remains Rembrandt’s “Portrait of Aeltje Uylenburgh”. The picture sold to an art dealer for $28.7 million in 2000 and then, for an undisclosed figure, to the van Otterloos in 2005. It has been displayed on loan, on and off, at the MFA since 2008.

“This is among the finest Rembrandts in private hands,” said MFA senior curator Ronni Baer as MFA workers completed renovations in the large gallery. “First of all it’s in pristine condition. You can tell the different shades of black and brown, which you can’t often see in Dutch pictures.”

“The fact that it’s now hanging here is so” — she took a deep breath — “is fabulous.”

At the Peabody Essex Museum, curators also feel a deep connection to the van Otterloo collection. Rose-Marie is vice president of the museum’s board of trustees and head of its collections committee. Eijk served as a trustee from 1994 to 2000.

The van Otterloos gave at least $10 million — they declined to say how much — to endow the museum’s directorship last year, and in 2011, PEM was the first institution to exhibit the couple’s collection of paintings and furniture in its entirety.

The museum does not have a curator dedicated to Dutch art. That could easily change, though, said director Dan Monroe. The museum is also planning a massive expansion, currently scheduled to be completed in 2017, which will include new galleries, education space, and collection storage. That is important because the van Otterloos say their collection must remain intact, including a 10,000-book collection that used to belong to retired Yale University professor Egbert Haverkamp-Begemann.

“We’re adding 175,000 square feet,” said Monroe. “The MFA’s last construction project was 130,000. So it if came down to whether we would have room for a collection like this, that’s clearly not a major issue.”

It appears not to be an issue for the MFA, either: In 2007, the MFA purchased the adjacent Forsyth Institute, a 107,000-square-foot building. The MFA plans to create a curatorial study and research area in that building, and the book collection would “fit absolutely perfectly,” Rogers said.

The couple’s relationship with the Harvard Art Museums is not as close, though Rose-Marie had high praise for director Tom Lentz, with whom the couple have also had a preliminary discussion about a potential gift. The Harvard Art Museums are in the midst of an expansion set to be completed next year.

“My guess,” said Lentz, “is it all depends on what they want to do with that collection. How do they want the collection used, and how do they want it perceived? If they like the grand state, they’ll go for something like the National Gallery or MFA. If they’re interested in a kind of research or teaching focus, they’ll look for somebody like us. To me, it’s a bit of a mystery because they’re very direct and forthcoming, but at the same time, they’re keeping their cards close to the vest.”

The gift will come with some requirements in addition to keeping the collection intact. The van Otterloos want any institution that accepts the collection to follow their philosophy. That means keeping the collection active, so the museum could purchase new works, even if it meant selling off lesser ones to pay for them.

It also means being generous with loans. This is something in which the van Otterloos have taken particular pride, with their works being shown all over the world. In her study, Rose-Marie keeps a binder stuffed with letters sent by people who have moved emotionally after seeing their collection in museums.

Their belief in sharing great art provides some comfort to museum directors. They know that even if the couple give the collection to just one institution, at least the works will remain in circulation.

“The van Otterloos have been very generous,” said Lentz. “Paintings come and paintings go. It’s very nice they give us full access to their collection. I think the most important thing is to have a good and long-term relationship. Ultimately, the decision is theirs.”

Correction: Because of a photographer’s error, captions accompanying an earlier version of this story misspelled the title of the painting “Orpheus Charming the Animals” and the collectors’ last name. Because of editing errors, the captions and story also may have misled readers about the exhibition of works from the collection in two galleries at the Museum of Fine Arts. The galleries contain 18 pieces from the van Otterloo collection of paintings and furniture, which was displayed in its entirety at the Peabody Essex Museum in 2011. One of the MFA galleries reopens Wednesday; the other reopened recently.

BostonGlobe.com complimentary digital access has been provided to you, without a subscription, for free starting today and ending in 14 days. After the free trial period, your free BostonGlobe.com digital access will stop immediately unless you sign up for BostonGlobe.com digital subscription. Current print and digital subscribers are not eligible for the free trial.

Thanks & Welcome to Globe.com

You now have unlimited access for the next two weeks.

BostonGlobe.com complimentary digital access has been provided to you, without a subscription, for free starting today and ending in 14 days. After the free trial period, your free BostonGlobe.com digital access will stop immediately unless you sign up for BostonGlobe.com digital subscription. Current print and digital subscribers are not eligible for the free trial.